Fraction Calculator

Add, subtract, multiply, or divide two fractions, with the exact simplified result

Adding, subtracting, multiplying, or dividing fractions and getting an exact simplified result — rather than a rounded decimal approximation — matters for any calculation where precision genuinely counts, since converting fractions to decimals and back introduces rounding error that exact fraction arithmetic avoids entirely.

Why exact fraction math beats decimal conversion

Many fractions don't convert to a clean, terminating decimal — a fraction like one-third becomes an infinitely repeating decimal, which any real calculation has to round somewhere, introducing a small but real inaccuracy. Performing arithmetic directly on fractions (finding a common denominator for addition/subtraction, or multiplying numerators and denominators directly for multiplication/division) avoids that rounding entirely, producing an exact result that can then be simplified to its lowest terms — a fraction whose numerator and denominator share no common factor beyond 1. For any calculation that later needs to be exact (a recipe scaled by a fraction, a precise measurement conversion, a construction or engineering calculation), working in exact fractions throughout avoids compounding small rounding errors across multiple calculation steps.

A worked example

Adding two fractions that don't share a denominator requires first converting them to a common denominator before adding numerators — doing this arithmetic in decimal form instead (converting each fraction to a decimal, adding, then trying to convert back to a fraction) can introduce rounding error that the exact fraction-arithmetic approach never encounters in the first place.

How this connects to your other math calculations

For numbers too large for standard calculator precision rather than fractional precision specifically, the Big Number Calculator handles a related but different class of precision concern — exact arithmetic on very large integers rather than exact arithmetic on fractional values.

Common mistakes

Converting fractions to decimals to perform arithmetic, then converting the decimal result back to a fraction, introduces avoidable rounding error at both conversion steps — for any calculation where an exact fractional result actually matters, working entirely in fraction arithmetic from start to finish avoids that compounding error.